Provider: Ingenta Connect
Database: Ingenta Connect
Content: application/x-research-info-systems
TY - ABST
AU - Heck, Daniel W.
TI - A caveat on the Savage–Dickey density ratio: The case of computing Bayes factors for regression parameters
JO - British Journal of Mathematical and Statistical Psychology
PY - 2019-05-01T00:00:00///
VL - 72
IS - 2
SP - 316
EP - 333
KW - Bayesian model selection
KW - marginal likelihood
KW - general linear model
KW - Jeffreys–
KW - Zellner–
KW - Siow prior
KW - Hypothesis test
KW - variable selection
N2 - The Savage–Dickey density ratio is a simple method for computing the Bayes factor for an equality constraint on one or more parameters of a statistical model. In regression analysis, this includes the important scenario of testing whether one or more of the covariates have an
effect on the dependent variable. However, the Savage–Dickey ratio only provides the correct Bayes factor if the prior distribution of the nuisance parameters under the nested model is identical to the conditional prior under the full model given the equality constraint. This condition
is violated for multiple regression models with a Jeffreys–Zellner–Siow prior, which is often used as a default prior in psychology. Besides linear regression models, the limitation of the Savage–Dickey ratio is especially relevant when analytical solutions for the Bayes
factor are not available. This is the case for generalized linear models, non‐linear models, or cognitive process models with regression extensions. As a remedy, the correct Bayes factor can be computed using a generalized version of the Savage–Dickey density ratio.
UR - https://www.ingentaconnect.com/content/bpl/bmsp/2019/00000072/00000002/art00006
M3 - doi:10.1111/bmsp.12150
UR - https://doi.org/10.1111/bmsp.12150
ER -